Proving Continuity

I have the function (a,b),U_{(a,b)})\rightarrow((c,d),U_{(c,d)})" alt="f(a,b),U_{(a,b)})\rightarrow((c,d),U_{(c,d)})" />, where is the subspace topology of the usual topology where A = (a,b) and is the subspace topology of the usual topology where A = (c,d), defined as

Why are polynomials continuous? It comes down to sum and product behavior of limits. Of course, this polynomial is actually linear, so you can probably hammer out an epsilon-delta just for this one case if you prefer.

Why are polynomials continuous? It comes down to sum and product behavior of limits. Of course, this polynomial is actually linear, so you can probably hammer out an epsilon-delta just for this case if you prefer.